A greedy non-intrusive reduced order model for fluid dynamics

We introduce a greedy non-intrusive reduced order method(ROM) for parameterized time-dependent problems with an emphasis on problems in fluid dynamics. The non-intrusive ROM is based on two-level proper orthogonal decomposition(POD) to extract temporal and spatial reduced basis from a set of candidates and a radial basis function(RBF) model to be used to approximate the coecients of the reduced model. And instead of adopting uniform or random sampling strategies, the candidates are determined using an adaptive greedy approach to minimize the overall computational online cost. Numerical studies are presented for a two-dimensional diusion problem and a driven cavity problem governed by incompressible Navier-Stokes equations. The results demonstrate that the greedy non-intrusive ROM predicts the flow field accurately and efficiently.